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Maru [420]
3 years ago
14

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

Mathematics
1 answer:
Nady [450]3 years ago
3 0
F(x) = x² + 4x + 10

f(x) - 10 = x² + 4x

perfect square:
x² + 4x + 4 ⇒ (x + 2)²

(x + 2)² = x(x+2) + 2(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

f(x) - 10 + 4 = x² + 4x + 4
f(x) - 6 = (x+2)²
f(x) = (x+2)² + 6
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Y=-4x + 2<br> y = -x - 1
USPshnik [31]

Hey there! I'm happy to help!

We have two values for y in terms of x. We can now create an equation to solve for what x is.

-4x+2=-x-1

We add x to both sides

-3x+2=-1

We subtract 2 from both sides.

-3x=-3

We divide both sides by -3.

x=1

Now, we can plug our x into one of the original equations and then solve for y!

y= -4+2

y=-2

We can also test this with the other.

y= -1-1

y=-2

Therefore, our solution is (1, -2), or x=1 and y=-2.

I hope that this helps!

7 0
3 years ago
Find the quotient. 800 ÷ 4
Art [367]

Answer:

200

Step-by-step explanation:

Hopw this helps! <3

3 0
3 years ago
Read 2 more answers
How can use base- ten blocks to find 2.16 divided by 3?
Lubov Fominskaja [6]
Youll have to move the decimal to the right twise on both of then them divide normally
3 0
3 years ago
Owen had 18 guitars. He sold 5 guitars and kept the rest. What is the ratio of guitars he kept to guitars he sold?
Romashka [77]

Answer:

to get what he kept subtract 5 from 18, to get 13 so 13 was kept. the ratio will be kept:sold which is 13:5

3 0
3 years ago
Read 2 more answers
According to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on ave
ki77a [65]

Answer:

The value of test statistics is 1.06.

Step-by-step explanation:

We are given that according to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on average. A random sample of 11 American teenagers was surveyed and the mean amount of time per month each teenager watched social media posts was 15.6. This data has a sample standard deviation of 2.5.

We have to test if the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year or not.

Let, NULL HYPOTHESIS, H_0 : \mu = 14.8 hours  {means that the mean amount of time American teenagers watch social media posts per month is same as the mean amount of time last year}

ALTERNATE HYPOTHESIS, H_1 : \mu > 14.8 hours  {means that the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year}

The test statistics that will be used here is One-sample t-test;

             T.S. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = sample mean amount of time per month each teenager watched social media posts = 15.6 hours

             s = sample standard deviation = 2.5 hours

             n = sample of teenagers = 11

So, <u>test statistics</u> =  \frac{15.6 - 14.8}{\frac{2.5}{\sqrt{11} } } ~ t_1_0

                            = 1.06

Hence, the value of test statistics is 1.06.

5 0
3 years ago
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